Find the value of the expression.
-Let $\log _ { b } A = 4$ and $\log _ { b } B = - 5$. Find $\log _ { b } 2 \sqrt { A B }$.
A) $- 0.500$
B) $- 4.472$
C) $4.472$
D) $2 \sqrt { - 20 }$

Question

Quizplus · Accepted Answer

Using the given logarithmic values and properties of logarithms, we can find the value of the expression. First, we know that $\log_b A = 4$ and $\log_b B = -5$. The expression $\log_b 2\sqrt{AB}$ can be rewritten using logarithm properties as $\log_b 2 + \frac{1}{2}\log_b AB$. Using the given values, this becomes $\log_b 2 + \frac{1}{2}(\log_b A + \log_b B) = \log_b 2 + \frac{1}{2}(4 - 5) = \log_b 2 - 0.5$. Since we don't have the value of $\log_b 2$, we cannot directly calculate a numerical value for the entire expression. However, the correct interpretation based on the given options and assuming a misunderstanding in the question's expectation for a specific numerical answer, the closest choice reflecting the manipulation of the given information is $-0.5$, which corresponds to choice A. This choice seems to be a direct interpretation of the calculation without considering the value of $\log_b 2$, which was not provided.

Find the Value of the Expression log⁡bA=4\log _ { b } A = 4logb​A=4

Find the Value of the Expression $\log _ { b } A = 4$